Known as "Big Bird," Robinson often dwarfed opposing players with his 6'4", 225-pound frame. Despite his imposing size, he was passed over three times by the Canadiens in the 1971 Amateur Draft. When they finally did take him as their fourth pick, he was only the 20th player selected overall. Ironically, two decades later, there were only two players from that draft active in the league - Robinson and Guy Lafleur - both Canadiens and both Hall of Famers.

Robinson was born and raised on a dairy farm in eastern Ontario. He played junior hockey for the Brockville Braves of the Ontario Junior Hockey League and the Kitchener Rangers of the Ontario Hockey Association. Robinson first turned professional with the Nova Scotia Voyageurs of the American Hockey League and helped them win the 1971-72 Calder Cup, the first Canadian-based team to do so. Later that year Robinson joined the Canadiens, winning his first Stanley Cup in his rookie year. He went on to help his team win the Cup many more times, including four in a row from 1976 to 1979 and one more in 1986. This last one was a surprise win for Montreal, and commentators remarked that Robinson seemed to come alive in the playoffs against the Boston Bruins after being elbowed by Bruin Louis Sleigher.

Robinson played 17 seasons for the Canadiens and then three more for the L.A. Kings, from 1989 to 1992. He won the Norris Trophy twice as the league's best defenseman in the 1976-77 and 1979-80 seasons and the Conn Smythe Trophy in 1977-78. Not only was Robinson a great defensive player, he was also very good with the puck. He held the NHL record for most playoff games at 227, until surpassed by Mark Messier, and the most consecutive years in the playoffs with 20. He also became a veritable regular in All-Star games, playing in 10 of them. His final NHL totals were impressive: 208 goals, 750 assists and 958 regular-season points as well as 144 points in 227 playoff games.

Internationally, Robinson represented Team Canada in the 1976, 1981 and 1984 Canada Cup tournaments. All three were Canadian victories. In 1981 he represented Canada in the World Championship and was named to the tournament All-Star team.

In 1993 Robinson was appointed assistant coach with the New Jersey Devils. Two years later, in 1995, the team won the Stanley Cup. Later that same year, Robinson was named head coach of the L.A. Kings, his former team. After leaving Los Angeles at the end of the 1998-99 season, Robinson signed as assistant in New Jersey. Midway through 1999-2000, head coach Robbie Ftorek was fired and Robinson came in and not only assumed coaching duties but took his team to Stanley Cup victory, his first as head coach.